connection%20formulas%20across%20transition%20points
(0.002 seconds)
1—10 of 396 matching pages
1: 36.4 Bifurcation Sets
…
►
§36.4(i) Formulas
… ► , cusp bifurcation set: … ► , swallowtail bifurcation set: … ►Elliptic umbilic bifurcation set (codimension three): for fixed , the section of the bifurcation set is a three-cusped astroid … ►Hyperbolic umbilic bifurcation set (codimension three): …2: 36.5 Stokes Sets
…
►where denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space.
…
►The Stokes set is itself a cusped curve, connected to the cusp of the bifurcation set:
…
►They generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set (§36.4).
…
►This part of the Stokes set connects two complex saddles.
…
►In Figure 36.5.4 the part of the Stokes surface inside the bifurcation set connects two complex saddles.
…
3: William P. Reinhardt
…
►This is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel.
…
►
…
►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
4: 25.12 Polylogarithms
5: 20 Theta Functions
Chapter 20 Theta Functions
…6: Bibliography O
…
►
Fourier Expansions. A Collection of Formulas.
Academic Press, New York-London.
…
►
An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
…
►
Connection formulas for second-order differential equations with multiple turning points.
SIAM J. Math. Anal. 8 (1), pp. 127–154.
►
Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities.
SIAM J. Math. Anal. 8 (4), pp. 673–700.
…
►
General connection formulae for Liouville-Green approximations in the complex plane.
Philos. Trans. Roy. Soc. London Ser. A 289, pp. 501–548.
…
7: Bibliography W
…
►
Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
…
►
The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
…
►
On the central connection problem for the double confluent Heun equation.
Math. Nachr. 195, pp. 267–276.
…
►
On the connection formulas of the fourth Painlevé transcendent.
Anal. Appl. (Singap.) 7 (4), pp. 419–448.
►
On the connection formulas of the third Painlevé transcendent.
Discrete Contin. Dyn. Syst. 23 (1-2), pp. 541–560.
…
8: Gergő Nemes
…
►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
…
9: Wolter Groenevelt
…
►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
…
10: Bibliography I
…
►
IEEE Standard for Floating-Point Arithmetic.
The Institute of Electrical and Electronics Engineers, Inc..
…
►
IEEE International Standard for Information Technology—Microprocessor Systems—Floating-Point arithmetic: IEEE Std 754-2019.
The Institute of Electrical and Electronics Engineers, Inc..
…
►
The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
…
►
The method of isomonodromic deformations and relation formulas for the second Painlevé transcendent.
Izv. Akad. Nauk SSSR Ser. Mat. 51 (4), pp. 878–892, 912 (Russian).
…
►
Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution.
J. Phys. A 31 (17), pp. 4073–4113.
…